Generalized Von Mises Density Function
Density for the Generalized von Mises circular distribution.
dgenvonmises(x, mu1, mu2, kappa1, kappa2)
x |
a vector. The object is coerced to class |
mu1 |
principal direction of the distribution. The object is coerced to class |
mu2 |
secondary direction parameter. The object is coerced to class |
kappa1 |
non-negative numeric parameter of the distribution. |
kappa2 |
non-negative numeric parameter of the distribution. |
The Generalized von Mises distribution has density
f(x)=exp[κ_1 \cos(x-μ_1) + κ_2 \cos{2(x-μ_2) }] / [2 π G_0(δ,κ_1,κ_2)],
for 0 <= x < 2 π, where δ=(μ_1-μ_2) and G_0 is the normalizing constant.
The density
Federico Rotolo
Gatto , R. & Jammalamadaka , S.R. (2007). The generalized von Mises distribution. Statistical Methodology 4, 341-353.
ff <- function(x) dgenvonmises(x, mu1=circular(5*pi/4), mu2=circular(pi/4), kappa1=.3, kappa2=1) curve.circular(ff, join=TRUE, xlim=c(-1, 1), ylim=c(-1.2, 1.2), main="Density of a Generalized von Mises Distribution", xlab=expression(paste(mu,"1=5/4",pi,", ",mu2,"=",pi/4,", ",kappa,"1=0.3, ",kappa,"2=1")) )
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